Wireless communications systems that employ spread spectrum technology, such as code division multiple access (CDMA) systems, transmit multiple calls within a single cell over a single carrier. CDMA systems use codes, rather than allocated times or frequencies, to distinguish between calls. CDMA 2000 1x and 3x systems encode calls using a Walsh code and pseudo-noise (PN) sequences. The Walsh code is used to distinguish one call from other calls transmitted from the same base station over the single carrier. Pseudo-noise (PN) sequences are used to distinguish one base station from other base stations. The PN sequences are also used to increase the bandwidth of signal transmitted by the base station. The increased bandwidth results in a number of advantages unique to spread spectrum systems, including improved call quality, increased call capacity, and enhanced security.
A base station encodes a call by modulating a digitized voice signal with a Walsh code and with in-phase pseudo-noise (I-PN) and quadrature-phase pseudo-noise (Q-PN) sequences. The base station then transmits a carrier signal containing multiple encoded calls. To receive a call, a mobile station must receive the carrier signal and multiply it with the correct Walsh code and PN sequences to filter out the desired voice signal. The mobile station must generate the same Walsh code and PN sequences as those in the carrier signal, and must adjust the frequency of the Walsh code and PN sequences generated by the mobile station to match those in the carrier signal.
A clock in the mobile station, such as a voltage-controlled temperature-compensated crystal oscillator (VCTCXO), controls the frequency of the Walsh code and PN sequences generated by the mobile station. The mobile station adjusts the frequency of the VCTCXO by a process called automatic frequency control (AFC). A rotation of signal constellation of in-phase and quadrature-phase outputs of a correlator in the mobile station indicates frequency error between the clock in the mobile station and the clock in the base station. In-phase correlator (I-C) output and quadrature-phase correlator (Q-C) outputs are determined for a chip length of, for example, 256 chips. The I-C and Q-C outputs for successive chip lengths may be plotted to illustrate the signal constellation. If there is no frequency error between the mobile station and the base station, the signal constellation remains stationary. However, if there is a frequency error, the signal constellation rotates around the origin.
FIG. 1 illustrates an example of a signal constellation 100 when there is a frequency error between the received signal and the reference signal. Correlator outputs 102 through 124 represent plots of the I-C and Q-C outputs after successive chip lengths. For example, correlator output 102 may represent a plot of the I-C and Q-C outputs after 256 chips. Correlator output 104 may represent a plot of the in-phase and quadrature-phase correlator outputs after another 256 chips. Due to the frequency error, correlator outputs 102 through 124 rotate around the origin.
The angle of rotation of signal constellation 100 is proportional to the frequency error between the CDMA signal and the reference signal. The direction of rotation of the signal constellation indicates whether the reference frequency of the VCTCXO is too fast or too slow. AFC uses the angle of rotation and the direction of rotation of the signal constellation to estimate the frequency error between the carrier signal and the reference signal and to adjust the frequency of the reference signal accordingly. FIG. 2 illustrates the angle of rotation 206 and the direction of rotation 208 of a signal constellation 200 when there is a frequency error between the CDMA signal and the reference signal. Correlator outputs 202 and 204 may correspond to correlator outputs 102 and 104 in FIG. 1 calculated after successive correlation lengths. AFC adjusts the reference frequency of the VCTCXO until angle of rotation 206 becomes zero.
AFC works well in CDMA systems that have a wide capture range, such as IS-95. However, AFC has difficulties in CDMA systems that have narrower capture ranges, such as CDMA 2000 1x and CDMA 2000 3x. The capture range of a CDMA system can be calculated using the following formula:           Δ        <            f      chip              2      ⁢                           ⁢              N        ·                  f          center                    where Δ is the capture range, fchip is the chip rate of the PN sequences, N is the correlation length, and fcenter is the center frequency of the base station transmitter. Using typical approximate values for a CDMA 2000 3x system, fchip equals 1,228,800, N equals 256, and fcenter equals 2,100,000. Therefore, for a typical CDMA 2000 3x system:|Δ|<1.1×10−6In other words, the capture range for a typical CDMA 2000 3x system is approximately 1.1 ppm.
If an initial frequency selected by the mobile station is outside of the capture range, the AFC system is unable to determine the direction of rotation of the signal constellation. FIGS. 3 and 4 illustrate signal constellations for a CDMA system in which the correlator output rotates around the origin by one hundred eighty degrees (180°) after each correlation length. When this happens, the AFC system cannot determine whether to increase or decrease the reference frequency generated by the VCTCXO. The AFC system may be unable to match the frequency of the reference signal to the frequency of the carrier signal transmitted by the base station. If the frequency of the reference signal does not match that of the carrier signal, the mobile station is unable to filter out the desired voice signal from the carrier signal.